Standard Quantum Limit and Heisenberg Limit in Function Estimation

Unlike well-established parameter estimation, function estimation faces conceptual and mathematical difficulties despite its enormous potential utility. We establish the fundamental error bounds on function estimation in quantum metrology for a spatially varying phase operator, where various degrees...

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Bibliographic Details
Published in:Physical review letters 2020-01, Vol.124 (1), p.010507-010507, Article 010507
Main Authors: Kura, Naoto, Ueda, Masahito
Format: Article
Language:English
Subjects:
Entanglement
Errors
Mathematical analysis
Metrology
Operators (mathematics)
Parameter estimation
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Summary:Unlike well-established parameter estimation, function estimation faces conceptual and mathematical difficulties despite its enormous potential utility. We establish the fundamental error bounds on function estimation in quantum metrology for a spatially varying phase operator, where various degrees of smooth functions are considered. The error bounds are identified in the cases of the absence and the presence of interparticle entanglement, which correspond to the standard quantum limit and the Heisenberg limit, respectively. Notably, these error bounds can be reached by either position-localized states or wave-number-localized ones. In fact, we show that these error bounds are theoretically optimal for any type of probe states, indicating that quantum metrology on functions is also subject to the Nyquist-Shannon sampling theorem, even if classical detection is replaced by quantum measurement.
ISSN:0031-9007
1079-7114
DOI:10.1103/physrevlett.124.010507